GHP: A Maple Package for Performing Calculations in the Geroch-Held-Penrose Formalism

We present a new symbolic algebra package, written for Maple, for performing computations in the Geroch-Held-Penrose formalism. We demonstrate the essential features and capabilities of our package by investigating Petrov-D vacuum solutions of Einstein's field equations.     

Shear-free Perfect Fluids in General Relativity: Gravito-magnetic Spacetimes

We investigate shear-free, perfect fluid solutions of Einstein's field equations in which the perfect fluid satisfies a barotropic equation of state p = p(w) such that w + p 0. We find that if the electric part of the Weyl tensor (with respect to the fluid flow) vanishes and the spacetime is not conformally flat then the fluid volume expansion is zero but the vorticity is necessarily nonzero. In addition, we show that if p = –w/3 then necessarily either the fluid expansion is zero or the fluid vorticity is zero.     

First Integrals of Shear-Free Fluids and Complexity

A single master equation governs the behaviour of shear-free neutral perfect fluid distributions arising in gravity theories. In this paper, we study the integrability of yxx=f(x)y2, find new solutions, and generate a new first integral. The first integral is subject to an integrability condition which is an integral equation which restricts the function f(x). We find that the integrability condition can be written as a third order differential equation whose solution can be expressed in terms of elementary functions and elliptic integrals. The solution of the integrability condition is generally given parametrically. A particular form of which corresponds to repeated roots of a cubic equation is given explicitly, which is a new result. Our investigation demonstrates that complexity of a self-gravitating shear-free fluid is related to the existence of a first integral, and this may be extendable to general matter distributions.     

Integration in the GHP Formalism II: An Operator Approach for Spacetimes with Killing Vectors, with Applications to Twisting Type N Spaces

Held has proposed a coordinate- and gauge-free integration procedure within the ghp formalism built around four functionally independent zero-weighted scalars constructed from the spin coefficients and the Riemann tensor components. Unfortunately, a spacetime with Killing vectors (and hence cyclic coordinates in the metric, and in all quantities constructed from the metric) may be unable to supply the full quota of four scalars of this type. However, for such a spacetime additional scalars may be supplied by the components of the Killing vectors. As an illustration we investigate the vacuum type N spaces admitting a Killing vector and a homothetic Killing vector. In a direct manner, we reduce the problem to a pair of ordinary differential operator master equations, making use of a new zero-weighted ghp operator. In two different ways, we show how these master equations can be reduced to one real third-order operator differential equation for a complex function of a real variable—but still with the freedom to choose explicitly our fourth coordinate. It is then easy to see there is a whole class of coordinate choices where the problem reduces essentially to one real third-order differential equation for a real function of a real variable. It is also outlined how the various other differential equations, which have been derived previously in work on this problem, can be deduced from our master equations.     

The GHP Formalism and a Type N Twisting Vacuum Metric with Killing Vector

It is shown that the formalism introduced byGeroch, Held and Penrose has a geometrical basis. Withthe help of the resulting insight a canonical splittingof the complex function which appears in the standard form of the Algebraically Special metrics isrealized. The results of this splitting are applied tothe problem of a (special) Type N vacuum metric with atwisting principle null direction. It is demonstrated that it is possible (but not feasable) to findthe metric without the use of differential equations. Anestimate of the size of the metric is given.     

The excitation energy spectrum of liquid He II based on theU-matrix theory

Summary In this paper, we apply theU-matrix theory to derive an explicit expression for the excitation energy spectrum of liquid⁴He. Using a model for the effective chemical potential for⁴He, we are able to produce an excitation spectrum which is very close to the observed one. The inverse of the effective mass,i.e. 1/m ^*, is obtained as a function of momentumk. The ratio between the effective mass and the mass of helium atom atk=2.0 ?⁻¹,i.e. near the roton depth, is found to bem ^*(k=2.0 ?⁻¹)/m _He=0.18298, while the ratio atk=1.0 ?⁻¹ ism ^*(k=1.0 ?⁻¹)/m _He=−0.17103. The theoretical result of the excitation spectrum is consistent with observational data.

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Riassunto In questo lavoro si applica la teoria della matriceU per dedurre un'espressione esplicita per lo spettro d'energia di eccitazione dell'⁴He liquido. Usando un modello per il potenziale chimico efficace per l'⁴He si è in grado di produrre uno spettro di eccitazione molto simile a quello osservato. L'inverso della massa efficace, cioè 1/m ^*, è ottenuto in funzione del momentok. Si trova che il rapporto tra massa efficace e la massa dell'atomo di elio ak=2.0 ?⁻¹, cioè vicino alla profondità del rotore, èm ^* (k=2.0 ?⁻¹)/m _He= =0.18298, mentre quello ak=1.0 ?⁻¹ èm ^* (k=1.0 ?⁻¹)/m _he=−0.17103. Il risultato teorico dello spettro di eccitazione è coerente con i dati sperimentali.

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Резюме В этой статье мы применяем теориюU-матрицы для вывода явного выражения для энергетического спектра возбуждений Зидкого⁴He. Используя модель для эффективного химического потенциала для⁴He, мы воспроизводим спектр возбуждений который оказывается очень близким к зкспериментально наблюдаемому. Вычисляется обратная величина эффективной массы, т.е. 1/m ^*, как функция импульсаk. Получено отношение эффективной массы к массе атома гелия приk=2.0 ?⁻¹, которое составляетm ^* (k=2.0 ?⁻¹)/m _He=0.18298, тогда как это отношение приk=1.0 ?⁻¹ равноm ^* (k=1.0 ?⁻¹)/m _He=−0.17103. Теоретический результат для спектра возбужений согласуется с имеющимися экспериментальными данными.

     

n-step optical simulation of the n-qubit state: Applications in optical computing

A method to implement optically 2ⁿ states in n steps, using n optical position bits, is presented. The implementation of the NOT and C-NOT operations, as well as the Fredkin-Toffoli and conditional sign change gates are also discussed.     

n-step optical simulation of the n-qubit state: Applications in optical computing

A method to implement optically 2ⁿ states in n steps, using n optical position bits, is presented. The implementation of the NOT and C-NOT operations, as well as the Fredkin-Toffoli and conditional sign change gates are also discussed.     

云计算技术在未来智能电网信息处理平台中的应用

未来的电网将会是一个高度自动化、智能化的电网,如此一个庞大、复杂的系统从发电、输电一直到变、配、用电的过程时刻都会生成海量的电能信息及设备运行状态数据,这就需要一个强有力的信息处理平台作为支撑,且这个平台应具有对海量数据的可靠存储、准确分析、实时同步更新及共享的功能,尤其是音视频等异构数据的分析与处理.云计算技术在大数据处理中具有得天独厚的优势,本文将云计算技术引入到未来智能电网的信息处理平台的建设中,针对未来智能电网信息处理平台的各项功能需求,对比目前电网信息处理平台的诸多瓶颈进行深层次的探讨,证明了将云计算技术应用到未来智能电网信息处理平台中的可行性。     

SOME EXAMPLES OF ALGEBRAIC GEODESICS ON QUADRICS. II

In this note we give new examples of algebraic geodesics on some two-dimensional quadrics, namely, on ellipsoids, one-sheet hyperboloids, and hyperbolic paraboloids. It appears that in all considered cases, such geodesics are rational space curves.     

Count Data Time Series Modelling in Julia—The CountTimeSeries.jl Package and Applications

A new software package for the Julia language, CountTimeSeries.jl, is under review, which provides likelihood based methods for integer-valued time series. The package’s functionalities are showcased in a simulation study on finite sample properties of Maximum Likelihood (ML) estimation and three real-life data applications. First, the number of newly infected COVID-19 patients is predicted. Then, previous findings on the need for overdispersion and zero inflation are reviewed in an application on animal submissions in New Zealand. Further, information criteria are used for model selection to investigate patterns in corporate insolvencies in Rhineland-Palatinate. Theoretical background and implementation details are described, and complete code for all applications is provided online. The CountTimeSeries package is available at the general Julia package registry.     

Effective Connections and Fields Associated with Shear-Free Null Congruences

A special subclass of shear-free null congruences (SFC) is studied, with tangent vector field being a repeated principal null direction of the Weyl tensor. We demonstrate that this field is parallel with respect to an effective affine connection which contains the Weyl nonmetricity and the skew symmetric torsion. On the other hand, a Maxwell-like field can be directly associated with any special SFC, and the electric charge for bounded singularities of this field turns to be self-quantized. Two invariant differential operators are introduced which can be thought of as spinor analogues of the Beltrami operators and both nullify the principal spinor of any special SFC.     

多孔介质中化学反应对非等粘流体混合过程影响的格子Boltzmann研究

利用格子Boltzmann方法和GPU计算技术,在孔隙尺度上模拟多孔介质中包含界面化学反应的粘性指进现象,定量分析化学反应对流体混合的影响.采用单浓度变量的双稳态模型来描述界面反应,而各向同性的多孔介质则通过四参数法生成.研究发现化学反应能减小指进界面厚度,抑制流体的混合,甚至会出现反混合现象,并且随着反应速率的增加,影响越明显.     

并行代数多重网格算法可扩展性能分析

对当今求解大型稀疏线性代数方程组最有效的迭代方法之--代数多重网格(AMG)算法的并行计算进行可扩展性能分析.给出一套并行计算可扩展性能分析方法,用于分析和指导并行迭代算法及实现技术的设计与优化并应用于并行AMG算法.分析表明,网格算子的平均模式大小和迭代过程的算法效率分别制约了AMG算法启动阶段和迭代求解阶段并行性能的发挥,成为该类算法急需解决的两个关键问题.     

The GHP conformai Killing equations and their integrability conditions,with application to twisting type N vacuum spacetimes

The conformai Killing equations in resolved form and their first and second integrability conditions are obtained in the compact spin coefficient formalism for arbitrary spacetimes. To facilitate calculations an operatorL is introduced which agrees with the Lie derivative only when operating on quantities with GHP weights (0,0). The resulting equations are used to find the conditions for the existence of a two dimensional non-Abelian group of homothetic motions in a twisting typeN vacuum spacetime. The equivalence of two such sets of metrics is established, metrics that were recently the subject of independent investigations by Herlt on the one hand and by Ludwig and Yu on the other.     

Relativistic Continuum Random Phase Approximation and Applications II. Applications

The fully consistent relativistic continuum random phase approximation （RCRPA） has been constructed in the momentum representation in the first part of this paper. In this part we describe the numerical details for solving the Bethe-Salpeter equation. The numerical results are checked by the inverse energy weighted sum rules in the isoscalar giant monopole resonance, which are obtained from the constraint relativistic mean field theory and also calculated with the integration of the RCRPA strengths. Good agreement between them is achieved. We study the effects of the self-consistency violation, particularly the currents and Coulomb interaction to various collective multipole excitations. Using the fully consistent RCRPA method, we investigate the properties of isoscalar and isovector collective multipole excitations for some stable and exotic from light to heavy nuclei. The properties of the resonances, such as the centroid energies and strength distributions are compared with the experimental data as well as with results calculated in other models.     

自适应结构网格上扩散方程隐式时间积分算法及其应用

提出一种自适应结构网格(SAMR)上求解扩散方程的隐式时间积分算法.该算法从粗网格到细网格逐层进行时间积分,通过多层迭代同步校正保证粗细界面的流连续和计算区域的扩散平衡.分析算法复杂度,并给出评估算法低复杂度的准则.典型算例表明,相对于一致加密情形,本文算法能够在保持相同计算精度的前提下,大幅度降低网格规模和计算量,且具有低复杂度.将算法应用于辐射流体力学数值模拟中非线性扩散方程组求解,相对于一致加密网格,SAMR计算将计算量下降一个量级以上,计算效率提高33.2倍.     

Foundation for Quantum Computing II

In this continuation of an earlier paper we develop further the theme of quantum logical specification and derive from it some apparently physically viable instantiations of potential quantum computing devices. Specifically, in the case of a one-parameter set of terms (or labels)—read as instants of time—we find, emerging quite naturally from the algebraic setup, the paradigm for a single qubit epitomized by the case of a two-state fermion interacting with an external single mode boson. This covers the cases: cavity QED, trapped ions, and, when the qubits are multiplexed appropriately, NMR based systems. (This case degenerates to one in which only bosons are relevant as in the case of pure bosonic harmonic oscillator models in the “dual rail” representation. Such models fly in the face of the logic itself, thus clearly revealing even at this level their well-known shortcomings as practical quantum computing devices. Here as elsewhere logical constraints apparently dominate physical ones.) In a final section we indicate briefly how this process exactly generalizes, in the case of a manifold of terms more general than the one-parameter case, to yield the notion of holonomic quantum computation. In the course of this investigation we find an interpretation of path integrals as limits of sequences of logical CUTS, thus establishing a link—though still tenuous—between ensembles of acts of quantum computation and Lagrangians.     

Part II. Algebraic tails in three-dimensional quantum plasmas

We review various exact results concerning the presence of algebraic tails in three-dimensional quantum plasmas. First, we present a solvable model of two quantum charges immersed in a classical plasma. The effective potential between the quantum charges is shown to decay as 1/r ⁶ at large distances r. Then, we mention semiclassical expansions of the particle correlations for charged systems with Maxwell-Boltzmann statistics and short-ranged regularization of the Coulomb potential. The quantum corrections to the classical quantities, from orderh ⁴ on, also decay as 1/r ⁶. We also give the result of an analysis of the charge correlation for the one-component plasma in the framework of the usual many-body perturbation theory; some Feynman graphs beyond the random phase approximation display algebraic tails. Finally, we sketch a diagrammatic study of the correlations for the full many-body problem with quantum statistics and pure 1/r interactions. The particle correlations are found to decay as 1/r ⁶, while the charge correlation decays faster, as 1/r ¹⁰. The coefficients of these tails can be exactly computed in the low-density limit. The absence of exponential screening arises from the quantum fluctuations of partially screened dipolar interactions.